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Rules of Ray Diagram for Representation of Images Formed

A thin biconv...

Question

A thin biconvex lens having radius of curvature $10 cm$ is placed as shown in figure. Calculate the focal length of the lens, if parallel rays are incident as shown.

A

\frac{120}{7} cm

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B

\frac{160}{7} cm

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C

\frac{180}{7} cm

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D

\frac{150}{7} cm

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Solution

The correct option is C $\frac{180}{7} cm$
As the lens is of converging nature, the parallel rays will converge at focus.

We know,
$\frac{μ_{3}}{v} - \frac{μ_{1}}{u} = \frac{μ_{2} - μ_{1}}{R_{1}} + \frac{μ_{3} - μ_{2}}{R_{2}}$

Here,
$μ_{1} = \frac{5}{4}, μ_{2} = \frac{5}{3}, μ_{3} = \frac{3}{2}$

$R_{1} = 10 cm$ , $R_{2} = - 10 cm$

So, $\frac{3 / 2}{v} - \frac{5 / 4}{\infty} = \frac{5 / 3 - 5 / 4}{10} + \frac{3 / 2 - 5 / 3}{(- 10)}$

$\Rightarrow v = f = \frac{180}{7} cm$

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